In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values "true" and "false", usually denoted 1 and 0 respectively. Instead of elementary algebra where the values of the variables are numbers, and the prime operations are addition and multiplication, the main operations of Boolean algebra are the conjunction "and" denoted as ∧, the disjunction "or" denoted as ∨, and the negation "not" denoted as ¬. It is thus a formalism for describing logical relations in the same way that ordinary algebra describes numeric relations. 

Boolean algebra was introduced by George Boole in his first book "The Mathematical Analysis of Logic" (1847), and set forth more fully in his "An Investigation of the Laws of Thought" (1854). According to Huntington, the term "Boolean algebra" was first suggested by Sheffer in 1913. 

Boolean algebra has been fundamental in the development of digital electronics, and is provided for in all modern programming languages. It is also used in set theory and statistics. 

Boole's algebra predated the modern developments in abstract algebra and mathematical logic; it is however seen as connected to the origins of both fields. In an abstract setting, Boolean algebra was perfected in the late 19th century by Jevons, Schröder, Huntington, and others until it reached the modern conception of an (abstract) mathematical structure. For example, the empirical observation that one can manipulate expressions in the algebra of sets by translating them into expressions in Boole's algebra is explained in modern terms by saying that the algebra of sets is "a" Boolean algebra (note the indefinite article). In fact, M. H. Stone proved in 1936 that every Boolean algebra is isomorphic to a field of sets. What are the answers to this following set of questions: 1. what did George Boole Introduce?
Answer: 1. George Boole

Problem: (CNN) -- Spanish champions Barcelona will kick off 2011 without the services of world player of the year Lionel Messi and key defenders Carles Puyol and Gerard Pique. 

Coach Pep Guardiola has given top scorer Messi permission to miss Sunday's home clash with Levante as his side seek to move five points clear of second-placed rivals Real Madrid in the La Liga standings. 

The club's website reported on Friday that the Argentina forward had been allowed to extend his holiday, so will be missing from the line-up for only the fourth time this season. 

Captain Puyol is ruled out with a groin injury that he picked up playing for Catalonia in the representative game against Honduras earlier this month, and may also miss next weekend's trip to Deportivo La Coruna. 

Spanish league strike called off 

His central defensive partner Pique is suspended after picking up his fifth yellow card this season in Barca's final league game of 2010, the 5-1 thrashing of city rivals Espanyol on December 18. 

However, Guardiola will be able to call on Argentine defender Gabriel Milito and young midfielder Jeffren Suarez, who have both returned to training. 

Milito had been sidelined since injuring his thigh in the Spanish Cup win over Ceuta on November 10, while the 22-year-old Jeffren suffered a groin problem in the Champions League match win over Rubin Kazan on December 7. 

Football's best and worst of 2010 

Meanwhile, Jose Mourinho's Real Madrid will return to action on Monday with a trip to seventh-placed Getafe. 
1. What injury was talked about?
2. What rivals were there?
3. When did they play?
4. Who won?
5. Who injured their leg?
6. When?
7. What was called off?
8. Who is a top scorer?
9. What was he allowed to do?
10. Why?
11. Who was not allowed to play?
12. For what?
13. who returns from training?
Answer: 1. a groin injury
2. Barca and Espanyol
3. on December 18.
4. Barca
5. Milito
6. on November 10
7. Spanish league strike
8. Messi
9. to miss Sunday's home clash
10. to extend his holiday,
11. Pique is suspended
12. for picking up his fifth yellow card
13. Gabriel Milito and Jeffren Suarez

question: When I was a little girl I lived in a place with no winter. It was always warm there. It never got cold. It never snowed. Sometimes it rained. Sometimes there was wind. But there was no snow on the trees or on the ground. There was no snow falling on our heads. There was no snow to make a snowman. 

My teacher's name was Mrs. Scott. One day in December, Mrs. Scott told us that we were going to make a snowman. We were excited! We wanted to see a snowman. We knew how a snowman looked. We knew a snowman was made of three snowballs. A snowman had to have a carrot nose and black eyes and buttons. A snowman had a hat and a scarf. We knew all these things. 

Mrs. Scott asked us to bring everything we needed to our classroom to make a snowman. Jimmy said, "I can bring the hat and the scarf." Anita said, "I can bring a carrot for the nose." Selma said, "I can cut out some black circles for the eyes and the buttons." Ricky asked, "But who can bring the snow?" 

Mrs. Scott said, "I know what to do." 

The next day all the children brought the things for the snowman. We did not know where Mrs. Scott would get the snow. Then she showed us. Our snowman is made of three bushes! Three bushes painted white! We put all the things on the bushes and it looked like a real snowman.
1. What did the teacher say the class would build?
2. what was her name?
3. and in what month was this?
4. what was the snowman made out of?
5. Who was bringing the accessories for it?
6. Who brought items for the head?
7. And what about for the face?
8. Why was there no white powder to use?
9. what was the temperature like?
10. was there any sort of precipitation?
11. what kind?
****
answer:
1. a snowman
2. Mrs. Scott
3. December
4. snowballs
5. the students
6. Jimmy
7. Anita
8. there was no winter
9. warm
10. Sometimes
11. rain